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We propose a new bootstrap-based online algorithm for stochastic linearbandit problems. The key idea is to adopt residual bootstrap exploration, inwhich the agent estimates the next step reward by re-sampling the residuals ofmean reward estimate. Our algorithm, residual bootstrap exploration forstochastic linear bandit (\texttt{LinReBoot}), estimates the linear reward fromits re-sampling distribution and pulls the arm with the highest rewardestimate. In particular, we contribute a theoretical framework to demystifyresidual bootstrap-based exploration mechanisms in stochastic linear banditproblems. The key insight is that the strength of bootstrap exploration isbased on collaborated optimism between the online-learned model and there-sampling distribution of residuals. Such observation enables us to show thatthe proposed \texttt{LinReBoot} secure a high-probability $\tilde{O}(d\sqrt{n})$ sub-linear regret under mild conditions. Our experiments support theeasy generalizability of the \texttt{ReBoot} principle in the variousformulations of linear bandit problems and show the significant computationalefficiency of \texttt{LinReBoot}.

Residual Bootstrap Exploration for Stochastic Linear Bandit